"Historical understanding very often depends upon our ability to recognize that, in the course of time, problems undergo subtle, and sometimes profound, changes in both formulation and substance." (Laudan, 1977, p. 241)
Ben Wood, Thorndike's student from 1919 to 1923, prepared a careful exegesis of Thorndike's essentials of a valid scale: objectivity, defined zero and unit, definition of function to be measured, consistency, and comparability. Wood claims that "practically all the material ... is taken from Thorndike's well-known treatise, or directly inferred from some of its propositions" (Wood, 1923, p.141 referring to Thorndike, 1913, p. 11-18). In spite of this, Wood adapts Thorndike's "scaling" tradition meaning of these measurement essentials to fit his own "test score" tradition. (Wood was previously a student of Truman Lee Kelley, a leading proponent of test reliability).
Both Thorndike and Wood consider objectivity the cornerstone of measurement. Thorndike views objectivity in a broad sense which included reliability and validity. In Thorndike's scaling tradition, objectivity is sought in the development of calibrated scales and variable maps that competent thinkers would agree upon as defining the latent variable. Wood's test score tradition leads him to focus instead on how tests can be scored reliably.
The development of scales with a defined zero and unit is important to both Thorndike and Wood. Wood's view reflects a test score tradition with a strong emphasis on test score reliability: "the essential quality of a good point of origin and of a good unit of measure is stability" (Wood p. 149). He recommends reporting test scores on a z- score scale with a sample mean to define the zero point and a sample standard deviation to define the unit of measurement. Thorndike recognizes that the zero point on the scale is arbitrary, and seeks to construct scales with units defined by a set of calibrated items. This view reflects a scaling tradition with close connections to Rasch measurement. Although Thorndike does not calibrate individuals and items onto an underlying latent variable scale simultaneously, he does attempt to develop calibrated scales that can be used to measure individuals.
Wood's third principle, that the function to be measured must be defined as adequately as possible, deals primarily with content validity. Wood emphasizes precise operational definitions of the variable measured and cautions against "the tendency to confuse identity of name with identity of function" (Wood p. 153). For Thorndike, the position of the facts on the item map of the latent variable plays the key role in defining the function measured: "An ideal scale, such as that for weight, is a series of perfectly defined amounts of a perfectly defined thing, the differences between any two of them being also perfectly defined, so that a series varying by steps of equal difference can readily be selected" (Thorndike, p. 13 and Wood, p. 150).
Consistency is defined by Thorndike and Wood as the unidimensionality of a scale. Thorndike thinks this so obvious that his discussion consists of two statements: "The series of facts used as a scale must be varying amounts of the same sort of thing or quality. This requirement needs no comment" (Thorndike p. 13 and Wood p. 153). Wood recommends inspecting test items in order to determine the consistency of the test, but, in his view, useful test scores can be obtained from any hodgepodge of combinations of items measuring visibly different content areas, such as reading and mathematics.
Comparability deals with what constitutes a useable scale. According to Wood, "a scale is valid only if it can be applied with reasonable ease and accuracy to the objects or facts to be measured" (Wood p. 157). But Wood's discussion of this principle is disjointed and difficult to understand because the test score tradition does not contain the concept of a calibrated item scale. Within Thorndike's scaling tradition, however, the idea of comparisons is fundamental. Items are calibrated through a comparison process, and the measurement of individuals is viewed as a comparison between an individual's ability and item difficulties on a latent variable scale. Consequently, "scales for mental and social measurements can be of great service in spite of gross inferiority [in ease of use and accuracy] to the common scales for physical facts" (Thorndike p. 16).
Thorndike's and Wood's theories of measurement offer important insights into major measurement problems identified in the first quarter of this century. Their theories illustrate how definitions of measurement problems changed as the dominant measurement tradition moved from a scaling tradition (Thorndike) to a test score tradition (Wood). Evaluation of "progress" in measurement theory depends on the measurement problem being addressed and the research tradition that underlies the evaluator's perspective.
Laudan L 1977. Progress and its problems: Towards a theory of scientific growth. Berkeley, CA: University of California Press.
Thorndike EL 1913. An introduction to the theory of mental and social measurements. 2nd Ed. Revised and Enlarged. New York: Teachers College
Wood BD 1923. Measurement in higher education. Yonkers-on-Hudson, NY: World Book Co.
Thorndike's scaling vs. Wood's scoring. Engelhard G Jr. Rasch Measurement Transactions, 1992, 5:4 p.182
Please help with Standard Dataset 4: Andrich Rating Scale Model
|Rasch Measurement Transactions (free, online)||Rasch Measurement research papers (free, online)||Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch||Applying the Rasch Model 3rd. Ed., Bond & Fox||Best Test Design, Wright & Stone|
|Rating Scale Analysis, Wright & Masters||Introduction to Rasch Measurement, E. Smith & R. Smith||Introduction to Many-Facet Rasch Measurement, Thomas Eckes||Invariant Measurement: Using Rasch Models in the Social, Behavioral, and Health Sciences, George Engelhard, Jr.||Statistical Analyses for Language Testers, Rita Green|
|Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar||Journal of Applied Measurement||Rasch models for measurement, David Andrich||Constructing Measures, Mark Wilson||Rasch Analysis in the Human Sciences, Boone, Stave, Yale|
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